D if fe re n t e v o lu ti o n fo r d if fe re n t m a s s e s

(1)

8–1

8 . M a s s iv e s ta rs

8–2 Massivestars1

D if fe re n t e v o lu ti o n fo r d if fe re n t m a s s e s

Evolutionofcentraltemperatureanddensityforstarsofdifferentmasses

8–3 Massivestars2

D if fe re n t e v o lu ti o n fo r d if fe re n t m a s s e s

initialmass

M /M

⊙

<

0

.

5verylowmassHeburningnotignited,nosignificant evolutionduringlifetimeofUniverse 0

.

5

.. .

2

.

3lowmassHeburningignitedindegeneratecore (heliumflash),noCburning 2

.

3

.. .

8intermediateHeburningignitedinnon-degenerate core,noCburning

>

8highmassHe,Cburning,ignitedinnon- degeneratecore→supernova 8–4 Massivestars3

E v o lu ti o n o f h ig h m a s s s ta rs ( M > 8 M

⊙

)

•lessthen2%ofallstars •Heburningignitesinnon-degeneratecore,likeintermediatemassstars (2.3M⊙<M<8M⊙) •carbonburningignitesinnon-degeneratecore •subsequentnuclearprocess(oxygenburning,siliconburning)inthecore •fusionprocesses(H,He,Cburning)continueinshellsources •finalstage:onionlikeshellstructure

(2)

8–5 Massivestars4

A d v a n c e d n u c le a r p ro c e s s e s

Carbonburning anumberofpossiblechannels: 12

C +

12

C

→24

M g + γ +

18

.

93

M eV (

∗

)

→23

M g + n

−2

.

61

M eV (

∗

)

→23

N a + p +

2

.

24

M eV (I )

→20

N e + α +

4

.

61

M eV (I I)

→16

O +

2

α

−0

.

11

M eV (

∗

)

lowprobabilityfor

(

∗

)

similarratesfor(I)and(II)(for

T

≈109

K

). Instantaneousreactionsofnewlyproduced

p

,

n

,

α

withotherelements,e.g. 12

C ( p, γ )

13

N ( e

+

ν )

13

C ( α ,n )

16

O

8–6 Massivestars5

A d v a n c e d n u c le a r p ro c e s s e s

Neburningphotodisintegration(T

>

109 K) 20

N e + γ

→16

O + α

−4

.

73

M eV

20

N e + α

→24

M g + γ +

4

.

58

M eV

Oxygenburning 16

O +

16

O

→32

S + γ +

16

.

54

M eV

→31

P + p +

7

.

68

M eV

→31

S + n +

1

.

45

M eV

→28

S i+ α +

9

.

59

M eV

→24

M g +

2

α

−0

.

39

M eV

8–7 Massivestars6

A d v a n c e d n u c le a r p ro c e s s e s

Siliconburning(

T >

3·109

K

) •Photodisintegration:Theradiationfieldcontainshighenergyphotonscapable ofdisintegratingSinucleiintolighternuclei,αparticles,protons,neutrons. •

p, n ,α

reactimmediatelywithothernucleiandformheavieratomicelements upto56

F e

. •Networkofnuclearreactionswithinversereactionsoccurringat(almost)the samerates⇒quasithermalequilibrium •⇒Nuclearstatisticalequilibrium 8–8 Massivestars7

A d v a n c e d n u c le a r p ro c e s s e s

Nuclearstatisticalequilibrium(NSE)duringSiburning •sequenceofreactionslike,e.g.: 28

S i+ α

⇋32

S + γ

32

S + α

⇋36

A r + γ

36

A r + α

⇋40

C a + γ

. . .

52

F e + α

→56

N i+ γ

•(56 Nidecayslaterto56 Feviatwoβ+ decays) •NSEincomplete:ironnucleistillstable(fornow) •⇒formationofirongroupelements

(3)

8–9 Massivestars8

N u c le a r s ta ti s ti c a l e q u ili b ri u m (N S E )

•Formaltreatmentofphotodisintegrationinequilibriumverysimilartothe treatmentofphotoionisationinequilibrium(Sahaequation) •e.g.“chemical”equilibriumofthereaction: 28

S i+ α

⇋32

S + γ

•equatechemicalpotentials:

µ

28Si

+ µ

α⇋

µ

32S •concentrationsaregivenby: n28Sinα nu32S

=

2πmrkT h2

3 2

ex p

−Q kT •

Q

isthedifferenceofbindingenergy:

Q = ( m

28Si

+ m

α−

m

32S

) c

2

=

6

.

59

M eV m

r

=

28·4 28+4

=

3

.

5isthereducedmassof28

S i+ α

underSiburningconditionsn(28Si) n(32S)≈4 8–10 Massivestars9

N u c le a r s ta ti s ti c a l e q u ili b ri u m (N S E )

• prevailingnucleiinNSEasafunctionoftemperature

8–11 Massivestars10

H ig h m a s s s ta rs

HST/NASA EtaCarinae,oneofthemostmassivestarsknownanditsnebula 8–12 Massivestars11

In te ri o r e v o lu ti o n o f a 1 5 M

⊙

s ta r

0–12.15Myr:Mainsequence(Hcoreburning)phase 12.15–13.7Myr:Hecoreburning,Hshellburning thestarbecomesaredsupergiant(RSG) >13.75Myr:Ccoreburning,HandHeshellburning

(4)

In te ri o r e v o lu ti o n o f a 1 5 M

⊙

s ta r S tr o n g m a s s lo s s d u ri n g R S G p h a s e

In te ri o r e v o lu ti o n o f a 6 0 M

⊙

s ta r

•Masslossbecomes moreandmoreim- portant(radiative pressure!) •Veryhighmassstars looss20...30%of theirmassduring theirmainsequence phase •Thehighmasslosspreventsveryhighmassstarsfrombecomingredgiants

In te ri o r e v o lu ti o n o f a 6 0 M

⊙

s ta r

•layersofHandHeburningmaterialareexposed H-burningmaterial:HeandNrich.Wolf-RayetstarstypeWN He-burningmaterial:CandOrich.Wolf-RayetstarstypeWC 8–16 Massivestars15

H ig h m a s s s ta r e v o lu ti o n

Hatchedareasindicatephasesofrelativelyslowevolution(mainsequenceand Hecoreburning,fromMaeder&Meynet,A&A182,243)

(5)

A d v a n c e d n u c le a r p ro c e s s e s

Theendgame:irondisintegration(

T >

5·109

K

) Eventually,temperaturesohighthatγphotonsenergeticenoughtobreakup ironexistintheradiationfield. 56

F e + γ

→13

α +

4

n

−100

M eV

•absorbsalargeamountofenergy •triggerscollapseofcore •initiatesthesupernovaexplosion 8–18 Massivestars17

H ig h m a s s s ta r e v o lu ti o n

OnionshellmodelThefinalshell structureofahighmassstarshortly beforecorecollapse •StartingfromtheoutsideH,He,C andO(simplifiedtooneshell)and Siburningshellsareoperating •Fedisintegrationhasstartedinthe core

H ig h m a s s s ta r e v o lu ti o n T im e s c a le s o f th e c o re b u rn in g p h a s e s fo r a 2 0 M

⊙

s ta r

mainsequence10Mill.years Heburning1Mill.years Cburning300years Oburning2 3years Siburning2days 8–20 Massivestars19

H ig h m a s s s ta r e v o lu ti o n

•NofurthernuclearenergysourcesinthecoreafterSiburning •photodisintegrationofironabsorbsenergy! 56

F e + γ

→13

α +

4

n

•Contractionofthestellarcoreuntil

T

c≈1010

K

,

ρ

c≈1010g cm3 •Electrongasisultra-relativisticdegenerate,

M

c

> M

Chandra •⇒nothingcanstopthecollapseofthecore. Thishappensin(

τ

ff≈40

m s

) •Collapsecanonlybestoppedwhenthestellarmatterreachesthedensityof atomicnuclei

ρ

C≈1014g cm3 •neutronisation •formationofaneutronstar

(6)

N e u tr o n is a ti o n

Freeneutronsdecaywithahalf-lifetimeof10.25min:

n

→

p + e

−

+ ν

e

+

1

.

3

M eV

⇒Maximumenergyofproducedelectrons:1.3MeV DegenerateelectrongaswithFermimomentum

p

F

= h

3ne 8π1 3 Fermienergy:

ǫ

F

( e ) = m

e

c

2

+ p

2 F

( e )

2

m

e

re sp . ǫ

F

( e ) = p

F

( e ) c

non-relativisticresp.ultra-relativistic NeutronsarestableiftheFermienergyofthedegenerateelectrongasisisin excessof1.3MeV,i.e.allquantummechanicalstatesarefilledupto1.3MeV. IfthegasisdensertheFermienergyishigherandneutronscanbeformedfrom protonsandelectronsviainversebetadecay. 8–22 Massivestars21

N e u tr o n is a ti o n

Underneutronstarconditions:protonsandneutronsatneutronstardensities arenon-relativisticdegenerate.Fermi-energies:

ǫ

F

( n ) = m

n

c

2

+ p

2 F

( n )

2

m

n

p

F

( n ) = h

3

n

n 8

π

1 3

ǫ

F

( p ) = m

p

c

2

+ p

2 F

( p )

2

m

p

F

( p ) = h

3

n

p 8

π

1 3 Electronsareultra-relativisticdegenerate(restmasssmallerbyfactor1835!):

ǫ

F

( e ) = p

F

( e ) c p

F

( e ) = h

3

n

e 8

π

1 3 Equilibriumbetweenneutronsandprotons/electronsisreachedwhen

ǫ

F

( n ) = ǫ

F

( p ) + ǫ

F

( e )

N e u tr o n is a ti o n

Equilibriumcondition:

ǫ

F

( n ) = ǫ

F

( p ) + ǫ

F

( e ) m

n

c

2

+ p

2 F

( n )

2

m

n

= m

p

c

2

+ p

2 F

( p )

2

m

p

+ p

F

( e ) c

substituting

p

F

( n ,p ,e ) = h

3nn,p,e 8π

1 3

m

n

c

2

+ h

2 2

m

n 3

n

n 8

π

2 3

= m

p

c

2

+ h

2 2

m

p 3

n

p 8

π

2 3

+ h c

3

n

e 8

π

1 3 Theneutronstarmatterisneutral,thus

n

p

= n

e.

h c

3

n

p 8

π

1 3

+ h

2 2

m

p 3

n

p 8

π

2 3 −

h

2 2

m

n 3

n

n 8

π

2 3

= m

n

c

2 −

m

p

c

2

=

1

.

3

M eV

N e u tr o n is a ti o n h c

3

n

p 8

π

1 3

+ h

2 2

m

p 3

n

p 8

π

2 3 −

h

2 2

m

n 3

n

n 8

π

2 3

=

1

.

3

M eV

Atypicalneutronstardensityof

ρ =

2·1014g cm−3correspondsto

n

n≈1·1038

cm

−3 . Theresultingelectron/protondensityis

n

e

= n

p

=

1 200

n

n Neutronsarethedominantconstituentofneutronstarmatterindeed.

(7)

8–25 Core-collapseSupernovae1

C o re -c o lla p s e S u p e rn o v a e

•mattercontinuesto“rain”ontothe proto-neutronstar •reflectionatthesurfaceofthehigh densitycore •⇒formationofanoutwardmoving shockfront •+additionalenergyinputfroma neutrinowind.Meanfreepathof neutrinoswithinmatterofdensity ofatomicnuclei<1km •⇒inversionofthedirectionof movement •⇒supernovaexplosion (corecollapsesupernovae) 8–26 Core-collapseSupernovae2

C o re -c o lla p s e S u p e rn o v a e

Supernova1987aintheLargeMagellanicCloud afterbefore

N e u tr o n s ta r

Remnant:neutronstar •degenerateneutrongas •⇒polytropicmodelanaloguesto whitedwarfs •⇒massradiusrelation •limitingmass:

M

Ch

=

M3√ 1.5 4π

hc Gm⁴ 3 H

3 2

µ

−2 e

=

5

.

836

µ

−2 n

M

⊙

=

5

.

73

M

⊙ M3=2.71(Lane-Emdenconstant forpolytropicindexn=3,seechap- ter5)Mass-radiusrelationforwhitedwarfs andneutronstars 8–28 Core-collapseSupernovae4

N e u tr o n s ta r

Correctionstothissimplepicture •Effectsfromgeneralrelativityareimportant •e.g.forthehydrostaticequation:Tolman,Oppenheimer,Volkoff •⇒decreaseslimitingmass •equationofstatefortheinterior:creationofexoticparticles(pions,hyperons, quarkplasma?)–understandingnotverygood •⇒decreaseslimitingmass(analoguestoionisation) •realisticlimitingmass:2...3M⊙

(8)

N e u tr o n s ta r

Structureofaneutronstar(hypothetical) 8–30 Core-collapseSupernovae6

T h e c ra b

TheCrabnebula(M1)—theremnantofSN1054 Theneutronstarinthecentreofthe crabnebula ESO/VLT